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The derivative of log {log [log (sin x)]} w.r.t. sin x is

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a
1sin xlog sin xlog log sin x
b
1log sin xlog log sin x
c
-1sin xlog sin xlog log sin x
d
-1log sin xlog log sin x

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detailed solution

Correct option is A

Now ddx(loglog(log(sinx)) =1log log sin xddx(log(log(sinx))) =1log log sin x1log sin xddx(log(sinx))  =1log log sin x1log sin x1sin xcos x Now required derivative =1log log sin x1log sin x1sin xcos xcos x  =1sin xlog sin xlog log sin x

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